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[R-sig-dyn-mod] Failed attempt to use modFit- part 2
2 messages · jose romero, Thomas Petzoldt
Hi, thanks for your extensive summary. Please note that emails containing only attachments are "scrubbed" by the mailing list software. Such messages are archived: https://stat.ethz.ch/pipermail/r-sig-dynamic-models/attachments/20121230/cb578886/attachment.pl ... but may not be sent to all subscribers. The 2 equation approach seems to be frequently used in the literature but is quite obvious: dy1/dt = -a * y1 + (b1-d1) * y1 dy2/dt = a * y1 + (b2-d2) * y2 For micro-organisms it may be assumed that sub-population y1 adapts to the medium and only y2 is growing. One may also assume that birth (b) and death (d) rates of population y1 are balanced (b1 - d1 = 0), so that its net growth rate r1 = 0 and can be omitted, while in population y2: r2 = (b2 - d2) > 0. The latter can now be replaced by a resource limitation term, extended by further stages, or simply be "cut off" with a logistic term: dy1/dt = -a * y1 dy2/dt = a * y1 + rmax * (1 - y2/K) * y2 A demographic interpretation may be found in Wikipedia: http://en.wikipedia.org/wiki/Demographic_transition ... but it is surely much more complex in reality - especially the mechanisms, and the value of K. So be careful with your interpretation. Thomas P.